Topological Quantum Field Theories from Subfactors

Vijay Kodiyalam, V.S. Sunder (Institute of Mathematical Sciences, Madras, India), V.S. Sunder (Institute of Mathematical Sciences, Madras, India) , Haim Brezis

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English

CRC Press
30 September 2020

Series: Chapman & Hall/CRC Research Notes in Mathematics Series

Pure mathematicians have only recently begun a rigorous study of topological quantum field theories (TQFTs). Ocneanu, in particular, showed that subfactors yield TQFTs that complement the Turaev-Viro construction. Until now, however, it has been difficult to find an account of this work that is both detailed and accessible.

Topological Quantum Field Theories from Subfactors provides a self-contained, explicit description of Ocneanu's construction It introduces and discusses its various ingredients with the distinct advantage of employing only genuine triangulations. The authors begin with axioms for a TQFT, go through the Turaev-Viro prescription for constructing such a TQFT, and finally work through Ocneanu's method of starting with a finite depth hyperfinite subfactor"" and obtaining the data needed to invoke the Turaev-Viro machine.

The authors provide a very concise treatment of finite factors of type and their bimodules and include details and calculations for all constructions. They also present, perhaps for the first time in book form, notions such as quantization functors and fusion algebras. Accessible to graduate students and others just beginning to explore this intriguing topic, Topological Quantum Field Theories from Subfactors will also be of interest to researchers in both mathematics and theoretical physics.

By: Vijay Kodiyalam, V.S. Sunder (Institute of Mathematical Sciences, Madras, India), V.S. Sunder (Institute of Mathematical Sciences, Madras, India)
Series edited by: Haim Brezis, Ronald G. Douglas (Texas A & M University)
Imprint: CRC Press
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 453g
ISBN: 9781138442108
ISBN 10: 1138442100
Series: Chapman & Hall/CRC Research Notes in Mathematics Series
Pages: 136
Publication Date: 30 September 2020
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Kodiyalam, Vijay